Problem: Simplify the following expression and state the condition under which the simplification is valid: $r = \dfrac{n^2 + 2n - 15}{n^2 - 3n}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 + 2n - 15}{n^2 - 3n} = \dfrac{(n + 5)(n - 3)}{(n)(n - 3)} $ Notice that the term $(n - 3)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n - 3)$ gives: $r = \dfrac{n + 5}{n}$ Since we divided by $(n - 3)$, $n \neq 3$. $r = \dfrac{n + 5}{n}; \space n \neq 3$